Structured Doubling Algorithms for Weak Hermitian Solutions of Algebraic Riccati Equations

In this paper, we propose structured doubling algorithms for the computation of weak Hermitian solutions of continuous/discrete-time algebraic Riccati equations. Under the assumptions that partial multiplicities of purely imaginary and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil, respectively, are all even, we prove that the developed structured doubling algorithms converge to the desired Hermitian solutions globally and linearly. Numerical experiments show that structured doubling algorithms perform efficiently and reliably.